cdfcau {lmomco} | R Documentation

## Cumulative Distribution Function of the Cauchy Distribution

### Description

This function computes the cumulative probability or nonexceedance probability of the Cauchy distribution given parameters (xi and α) of the distribution provided by `parcau` or `vec2par`. The cumulative distribution function of the distribution is

F(x) = frac{arctan(frac{x - xi}{α})}{π}+0.5 mbox{,}

where F(x) is the nonexceedance probability for quantile x, xi is a location parameter and α is a scale parameter.

### Usage

    cdfcau(x, para)

### Arguments

`x` | A real value.
`para` | The parameters from `parcau` or `vec2par`.

### Value

Nonexceedance probability (F) for x.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.

### See Also

`quacau`, `parcau`, `vec2par`

### Examples

      para <- c(12,12)
      cdfcau(50,vec2par(para,type='cau'))

[Package lmomco version 0.92 Index]